The difference between pattern and structure coefficients lies in what aspect of the relationship between a variable and a factor they represent: pattern coefficients show the unique contribution, while structure coefficients indicate the total correlation.
Understanding Pattern Coefficients
Pattern coefficients are akin to standardized partial regression coefficients. They represent the unique, direct contribution of a factor to a measured variable, controlling for the influence of other factors in the model. In simpler terms, they tell you how much a variable loads onto a specific factor when the overlap with other factors is accounted for.
- Interpretation: They reflect the direct effect of a factor on a variable, similar to a regression weight.
- Nature: They are not simple factor-variable correlations; rather, they are similar to standardized partial regression coefficients, indicating the unique variance a factor explains in a variable.
- Primary Use: Essential for interpreting the unique composition of factors, especially in oblique (correlated) factor rotations where factors are allowed to relate to each other.
Understanding Structure Coefficients
Structure coefficients represent the simple bivariate correlation between a factor and a measured variable. They capture the total relationship, including both the direct influence of the factor and any indirect influence mediated through correlations with other factors.
- Interpretation: They are correlations between common factors and the measured variables. They show the total shared variance between a variable and a factor.
- Nature: Simple Pearson correlations between the latent factor and the observed variable.
- Primary Use: Valuable for understanding the overall context of a variable's relationship with a factor, providing insight into the comprehensive meaning of the factor.
Key Distinctions: Pattern vs. Structure Coefficients
The table below summarizes the core differences between pattern and structure coefficients:
| Feature | Pattern Coefficients | Structure Coefficients |
|---|---|---|
| Interpretation | Unique contribution of a factor to a variable | Total correlation between a factor and a variable |
| Nature | Similar to standardized partial regression coefficients | Simple bivariate correlations |
| Focus | Direct effects, unique variance explained | Total shared variance, direct and indirect effects |
| When to Use | Primarily for interpreting factor composition in oblique rotations, identifying which variables uniquely define a factor | For understanding the overall relationship of a variable with a factor, providing a broader context of the factor's meaning |
| Value Range | Can be above 1 or below -1 in specific cases, though typically between -1 and 1 | Always range between -1 and 1 |
When to Use Each: Practical Insights
Both pattern and structure coefficients are crucial for a comprehensive understanding of factor analysis results, especially in studies employing oblique factor rotations (where factors are allowed to be correlated).
- For defining factors: Pattern coefficients are often the primary focus for interpreting what a factor uniquely represents. If a variable has a high pattern coefficient on Factor 1 and low on Factor 2, it strongly contributes uniquely to Factor 1.
- For understanding factor meaning: Structure coefficients provide a broader picture. A variable might have a low pattern coefficient on a factor but a high structure coefficient, indicating it still correlates strongly with that factor, perhaps indirectly through its correlation with another factor that does uniquely load onto the first factor. This tells you the variable is related to the factor, even if it doesn't define it uniquely.
- Example: Imagine a survey on "job satisfaction" with factors like "Work Environment" and "Compensation." An item "My salary is fair" might have a high pattern coefficient on "Compensation." However, if "Compensation" and "Work Environment" are correlated, this item might also show a notable (but lower) structure coefficient with "Work Environment," because salary fairness can indirectly influence the perception of the work environment.
The Relationship Between Them
In models where factors are correlated (oblique rotations), structure coefficients are mathematically derived from pattern coefficients and the correlations between the factors themselves. Specifically, a structure coefficient for a variable on a factor is the sum of its pattern coefficient on that factor plus the pattern coefficients on all other factors multiplied by the correlations between those factors and the factor in question. This shows how structure coefficients encompass both direct and indirect relationships.
